The aim of this work is to construct the stochastic calculus of variations on Poisson space and some of its applications via the stochastic analysis on Wiener space. We define a new gradient operator on Wiener space, whose adjoint extends the Poisson stochastic integral. This yields a new decomposition of the Ornstein-Uhlenbeck operator and a substructure of the standard Dirichlet structure on Wiener space, with applications to stochastic analysis on Poisson space and infinite-dimensional analysis for the exponential density. (C) 1995 Academic Press, Inc. [References: 19]
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